On average, people breath 10,000 times per night with a standard deviation of 1400. You study 50 people and record how many breaths they take per night. What is the probability that the average of all participants in the study was fewer than 10,200 breaths each night?I want answer with step by step.

I WILL FIND THE GRADIENT FIRST

[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{5 - ( - 8)}{8 - 4} \\ m = \frac{5 + 8}{4} \\ m = \frac{13}{4} [/tex]

THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

I will use the point (8,5)

to find the value of c

[tex]5 = \frac{13}{4} (8) + c \\ 5 = \frac{104}{4} + c \\ c = 5 - \frac{104}{4} \\ c = - \frac{84}{4} \\ c = -21[/tex]

THE EQUATION IS

[tex]y = \frac{13}{4} x - 21[/tex]

We know the domain is the set of all x when is represented by ordered pairs: (x, y)

In this case {(-8,-12),(4,-8), (2, -10),(-10.-16) } we can observe that there are four x (the first number of each pair):

Domain = { -8, 4, 2, -10}

Answer:

3(x-5) =3x - x - 8

3x-15 = 2x - 8

3x-2x= -8+15

x=7

Step-by-step explanation:

first 3 will multiply by x and -5,which are in bracet like this

                                         3(x-5)= 3x - x -8

after they would became 3x-15 = 2x (because 3x will be subtracted by x) -8

                                           so it will become like this

                                             3x-15=2x-8

after that 3x will be subtracted by 2x like this 3x-2x and -8 will be add in +15 so it would be

                                    x=7

Consider that a rotation of 90° clockwise is given by:

T(x,y) => (y,-x)

The coordintates of the point L is L(0,1), the, after the rotation you have:

T(0,1) => (1,0)

answer:

D. L(1,0)

Answer:

(g ∘ f)(6) = 216

Step-by-step explanation:

We are given the functions f(x) = 2x - 6 and g(x)=x³

We want to find the value of (g∘f)(6), where we first find the value of f(6), and then substitute that value into g(x).

Substitute 6 as x in f(x)=2x-6.

f(6)=2(6)-6

Multiply

f(6)=12-6

Subtract

f(6)=6

Now substitute 6, which is the value of f(6) as x in g(x) = x³.

g(6)=6³ = 6 * 6 * 6 = 36 * 6 = 216

The value of g(6) is the same as the value of (g ∘ f)(6), as the 6 that we plugged into g(x) is the value of f(6).

Therefore, (g ∘ f)(6) = 216.

Answer: g/15 = 3 ; g = 45 gifts.

Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.

g/15 will equal 3.

Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).

This will get you the answer 45.

So, you will get the answer choice A.

Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .

In the question ,

we have to find , whether a Right Triangle can be made by two fractions and an integer length .

yes, we can make a Right Triangle with two lengths as fractions and other length as integer .

let us prove it with the help of an example .

Consider the triplet 7 , 24 , 25 .

let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be  1 .

We know that for the Right Triangle

(side1)² + (side2)² = hypotnuse²

(7/25)² + (24/25)² = 1²

49/625 + 576/625 = 1

(49+576) / 625 =1

625/625 = 1

1 = 1

hence ,it is a Right Triangle .

Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .

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The product of the given expression is 1,30,200.

Given expression:-

(−310)(4.2)(−100)

We have to find the solution of the given expression by using either the commutative property or the associative property.

We will use the associative property of multiplication to find the product.

(−310)(4.2)(−100) = (-310)*(4.2*(-100)) = (-310)*(-420) = 1,30,200

Associative property

The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.

Hence,

(a*b)*c = a*(b*c) , where a, b and, c are real numbers.

Commutative property

Commutative property In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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The equations are solved to give;

46. x = 5

48. h = 1

50. The inequality is 7 ≤ d/ -5

An algebraic expression is described as a mathematical expression that is composed of terms, factors, coefficients, constants and variables.

They are described as expressions made up of arithmetic operations which includes;

Given the expression;

46.  |2x + 5| = 3x

Take the absolute value, we have;

2x + 5 = 3x

collect like terms

2x - 3x = - 5

-x = -5

x = 5

48.  (3h + 8) + 2 = 13

expand the bracket

3h + 8 + 2 = 13

collect like terms

3h = 13 - 10

3h = 3

Make 'x' the subject of formula

h = 1

50. Seven is at most the quotient of a number d and -5.

This is expressed as;

7 ≤ d/ -5

Hence, the values are x = 5, h = 1 and 7 ≤ d/ -5

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Answer:

$134.50

Step-by-step explanation:

4200 x .035 = 134.50

3.5% Percent means per 100

3.5/100 when you divide by 100, you move the decimal two places to the left.

The commission amount is $147

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.

He sold $4200.

So, 3.5% of commission:

4200 x 3.5  / 100

= 147

Therefore, the commission is $147.

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Answer:

125

Step-by-step explanation:

71.47 rounded to the nearest whole number would be 71.

54.357 rounded to the nearest whole number would be 54.

Now, when we add 71 and 54, we get:

71+54=

125

The total would be 125

Answer:

8/15(-2/3)

we simply multiply them

-8*2/15*3

as we know that+*-=-

-16/30

so simply divided by 2 because it whole decide them 16/2and30/2

-8/15

Answer:

Step-by-step explanation:

gas mileage = miles covered/gallons used

but:

miles covered = [tex]35\frac{1}{2}[/tex]

                        = 35.5

gallons used     = 1[tex]\frac{1}{2}[/tex]

                           = 1.5

gas mileage = 35.5/1.5

gas mileage = 23.667 miles/gallon (to 3 decimal places)

gas mileage = miles covered/gallons used

but:

miles covered = [tex]27\frac{1}{5}[/tex]

                        = 27.2

gallons used     = [tex]\frac{4}{5}[/tex]

                         = 0.8

gas mileage = 27.2/0.8

gas mileage = 34 miles/gallon

c)

gas mileage of blue: 23.667 miles/gallon implies the blue car will travel 23.667 miles on 1 gallon

gas mileage of silver: 34 miles/gallon implies the silver car will travel 34 miles on 1 gallon

Hence the silver car would travel a greater distance on 1 gallon than the blue car.

A few properties of a parallelogram.

1) Opposite sides are always equal.

2) Opposite angles are always equal.

3) The sum of all the angles is 360.

In part 2, we are given the angles. Therefore, we can apply the 2nd property.

11x = 55

5y = z (lets say the unknown is z).

Now, 11x = 55

x = 55/11

x = 5

Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.

55 + 55 + 5y + z = 360

110 + 5y + z = 360

5y + z = 360 -110

5y + z = 250. (i)

According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get

5y + z = 250

z + z = 250

2z = 250

z = 250/2

z = 125

From the value of z, we can find the value of y using z = 5y

125 = 5y

5y = 125

y = 125/5

y = 25

Hence, x = 5 and y = 25

The number with 3,4 and 8 as its factors is 24

The least common multiple(LCM) can be defined as the smallest multiple that two or more numbers have in common

The Lowest Common Multiples of 3 are:3, 6, 9, 12, 15, 18, 21, 24, 27 and 30

The Lowest Common Multiples of 4 are:  4, 8, 12, 26, 20, 24, 28, 32, ...

The Lowest Common Multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

From the Lowest Common Multiples above, 24 is the only number that is common among the multiples of 3,4 and 8

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Of the functions listed in the options the ones that are linear are:

a. y = -2x

b. -4y = 3x

d. 2x - 3y = 12

Linear equations are equations of the first order. These equations are defined for lines in the coordinate system.

Answer:

The answers are all below.

Step-by-step explanation:

7. Yes

Plug 10 in for t

10-3 ≥ 2

7 ≥ 2

8. No

Plug 1 in for w

6(1) < -2

6 < -2 (Nope)

9. Yes

Plug 5 in for p

5 + 1.6 ≤ 4

6.6 ≤ 4

10. Yes

Plug 0 in for d

[tex]\frac{1}{2}[/tex](0) > -3

0 > -3

11.

1(------------------>k

12.

n<------------------]2.5

13.

In order to try out for one of the parts in a play at the local theater, you must be at most 12 years old. Write an inequality that represents this situation.

x≤12

x<-----------------]12

14. Yes

Plug 2 in for h

3(2) - 7 < 2

Simplify

6 - 7 < 2

-1 < 2

15. No

Plug -12 in for q

-12 + 8 ≥ [tex]\frac{-12}{4}[/tex]

Simplify

-4 ≥ -3 (Nope)

16.

    a. Yes

    Plug 0 in for x

    -2(0) < 10

    and

    -6 < -2(0)

    Simplify

    0 < 10

    and

    -6 < 0

    b. No

    Plug 4 in for x

    -2(4) < 10

    and

    -6 <  -2(4)

    Simplify

    -8 < 10

    -6 < -8 (Nope)

    c. -1

    Plug -1 in for x

    -2(-1) < 10

    and

     -6 < -2(-1)

    Simplify

    2 < 10

    and

    -6 < 2

The given equation is expressed as

Explanation

Step 1

the sum of the internal angles in a triangle equals 180, then

for triangle CDE

Step 2

as we can see, in poitn c, we have a 180 degrees angle(ACD)

so

I hope this helps you

The area of the rectangle is 104 inches²

Define Area of Rectangle

The area of a rectangle is the space occupied by the rectangle inside its perimeter.

Given that, the perimeter is 42 inches

we know, the formula of perimeter of rectangle = 2(L + W)

so, the first equation will be

2(L + W) = 42

or, 2L + 2W = 42       ----------eq(i)

Next, the length of a rectangle is 5 inches longer than its width, so

L = W + 5

or, L - 5 = W              --------------eq(ii)

Now, the eq(i) is

2L + 2W = 42

Put W value from eq(ii),

2L + 2(L- 5) = 42

=> 2L + 2L - 10 = 42

=> 4L - 10 = 42

=> 4L = 52

=> L = 13

We got, L = 13 put this value in any of the equation

I'm putting the value in eq(ii) as it easy for to solve

=> 13 - 5 = W

=> W = 8

If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that

2(13) + 2(8) = 42  (correct)

13 - 5 = 8 (correct)

Now, we got length and width so now just put the values of L and W in area of rectangle formula,

Area of rectangle = Length * width

                            = 13 * 8

Area of rectangle = 104 inches²

Hence, The area of the rectangle is 104 inches²

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The equation

has slope -3/7.

The product of perpendicular lines must be -1, so the slope of the new equation must be:

The line with that slope and that passes throught (1,6) is:

The following graph shows both equations:

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expressions are,

1. (14⁴)² × 14⁻⁶ / 14²

2. 14⁻⁵ (14³)² 14⁻²

3. (14³)⁴ (14⁻⁷)²

Now,

The solutions of the expressions are find as;

1. (14⁴)² × 14⁻⁶ / 14² = 14⁸ × 14⁻⁶ / 14²

                            = 14⁸⁻⁶ / 14²

                            = 14² / 14²

                            = 14²⁻²

                            = 14⁰

                            = 1

And,

2. 14⁻⁵ × (14³)² × 14⁻² = 14⁻⁵ × 14⁶ × 14⁻²

                               = 14⁻⁵⁺⁶⁻²

                               = 14⁻¹

                               = 1 / 14

And,

3. (14³)⁴ (14⁻⁷)² = 14¹²  14⁻¹⁴

                     = 14¹²⁻¹⁴

                     = 14⁻²

                     = 1 / 14²

                     = 1 / 196

Therefore,

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

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Given:

Required:

To

Answer:

Explanation:

The slope-intercept form of the equation of a line can be written as;

where m = slope of the line

b = y-intercept of the line

So if Joanne graphed a linear function with a slope(m) of -4 passing through (0, -2), let's go ahead and determine the y-intercept of the line as shown below;

Therefore, the equation of line will be y = -4x - 2 as graphed below;

Given Nick's function as y = -2x - 4, combining both graphs, we'll have the below;

The red line is Joanne's line while the blue line is Nick's line.

We can see from the above graph of both lines that Joanne's line intersects the y-axis above Nick's line's

The total price of that Ingrid has to pay is $52.90.

From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

Sales price = $48.90

Amount needed to be paid = 8.5% of $48.90 + $48.90

= 4.15 + $48.90

= $52.90

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Answer:

-0.5f - 4.52 = -25.52 + 1f

-1.5f = 21

f = 14

Answer:

14

Step-by-step explanation:

-4.52 + 25.52 = f + 0.5f

21 = 1.5f

f = 14

Answer:

Its A

Step-by-step explanation:

that's literally what a segment is

Answer:

Step-by-step explanation:

Since City a is an equation, you would have to solve it for its population, which is 280000, and since City B is 1,620,000 and City C is double city B, 3,240,000/280000 would get you the population, which is:

11.57, you would round up after that, which would get you the answer:

12

The ordered pairs that could be included in the set so that the relation remains a function of x is  (-6, 1), (-1, 1).

For the given relation that is a function of x.

{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}

As, from the definition of the function, the domain of the function will not repeat in the set.

Thus, (-6, 1), (-1, 1) is the ordered pairs that could be included in the set so that the relation remains a function of x.

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Answer: x=17

Step-by-step explanation:

Simplifying

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

The value of x in the equation is 17 .

Given,

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

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